Problem: What fraction of $\frac{1}{2}$ is $\frac{1}{7}$?
Solution: This problem is asking for $\frac{\frac{1}{7}}{\frac{1}{2}}$.  (More advanced students can analyze this alternatively by rewriting this worded statement as an equation, we have $x \cdot \frac{1}{2} = \frac{1}{7}$, where $x$ is the fraction of $\frac{1}{2}$ that we are solving for.  Dividing both sides by $\frac{1}{2}$, we have $x = \frac{\frac{1}{7}}{\frac{1}{2}}$).  We can simplify this fraction as $\frac{1}{7} \cdot \frac{2}{1}$, since division is the same as multiplying by the reciprocal.  Multiplying these two fractions then yields $\boxed{\frac{2}{7}}$.